Note on tense SHn–algebras

Abstract. In this article, we continue the study of tense SHn–algebras [5]. These algebras constitute a generalization of tense ÃLukasiewicz–Moisil algebras [4]. In particular, we describe a discrete duality for tense SHn–algebras bearing in mind the results indicated by OrÃlowska and Rewitzky in [13], for SHn–algebras. In addition, we introduce a propositional calculus and prove this calculus has tense SHn–algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus. 2010 Mathematics Subject Classification. Primary 03G25; Secondary 03B44. Key words and phrases. SHn–algebras, tense SHn–algebras, discrete duality